The Sky *was* Falling

On Monday, March 26, a Chilean flight to New Zealand was almost struck by falling bits of space something. The pilot of the flight noted he could see burning up materials both in front and behind the flight. (Information obtained from numerous news sources). Some reports attributed the falling carnage to a Progress M-58 burning up through the atmosphere as it returned from the International Space Station, or at least insinuated as much. In fact, there had been an alert that such a re-entry would be occurring. According to US space officials, however, at the time of the incident the Progress was still attached to the ISS, and no set of calculations can make a Progress be in two places at once. The US Space Surveillance Network had no reports of other re-entering space junk. With all known space junk ruled out, it looks like that airplane was almost almost hit by an asteroid.

That silly little kid in me wishes I had been on that airplane. They could actually hear the fragments burning up.

Should I worry about meteors when I fly? Nope. And doing stats can be fun.
Time for some back of the envelope calculations. Say that 2 asteroids a year crash through the atmosphere like the one seen by this flight. This is a total guesstimate. I’m sure a real number is out there somewhere, but I’m feeling lazy. Let’s say those two estimated asteroids turned meteorites spend roughly 30 seconds falling in bits and pieces through airplane altitudes. That would be 1 minute a year out of 365.24d*24hr/d*60min/hr = 525949 minutes/year. So, the probability of an asteroid going through the atmosphere at any one moment is 1 in 525949.

Now, that falling piece of rock broke up and splatted through the atmosphere over an area of roughly 100 square kilometers. Assuming the plane is at a cruising altitude around 35,000 ft (10.7 km) above our Earth (radius = 6,378.1 km), there is a total area of 4 pi r^2 = 512,918,602 square km. So, the probability that one particular plane will be within that 100 square km is 1 in 5,129,186.

Put together the probability that at any given half minute in time a plane will be at in the particular 100 square km region is those two probabilities multiplied together: 1 in 2,697,690,256,973.

Now, that assumes there is one plane hanging out flying. I tried to find out how many planes are flying at any given moment and failed. According to the National Air Traffic Controllers Associationroughly 87,000 flights a day fly over the US alone. Based on that, I’m going to make a wild guess that at any given moment there are probably an average of 10,000 flights some where. They aren’t evenly distributed. For instance, you’ll get more flights over the East Coast instead of over Antarctica. I’m going to ignore that however, to get a worst case approximation. Let’s say those guesstimated 10,000 flights are distributed evenly over the planet. That gives us a 1 in 269,769,025 (likely severely exaggerated) chance that an airplane will get hit by a meteor.

So, yeah, I’m not worried 🙂

Now, I have to admit that stats is one of those places where I periodically leave out details. If anyone knows what I left out, please leave a comment.